Consider a market in which there are two firms, both producing the same good. Firm i's cost of producing qi units of product is :

Ci(qi) = qi^2 for i = 1, 2.

The price at which output is sold when the total output is q1 + q2 is:

Pd(q1 + q2) = q1 q2 for all q1 + q2 .

Each firm's strategic variable is output, as in Cournot's model, but the firms make their decisions sequentially, rather than simultaneously: firm 1chooses its output, then firm 2 does so, knowing the output chosen by firm 1.

Find the subgame perfect equilibrium of this Stackelberg's duopoly.